Heat the over to 425°F. On a lightly floured work surface, roll the pastry to a 10x14-inch rectangle. Using the back of a spoon, spread the pastry evenly with the mustard. Sprinkle on the Gruyère and Parmigiano in an even layer.
Arrange the ham in a single, even layer, tearing or cutting pieces to fit. Lay a piece of parchment or waxed paper on top and gently roll and press with the rolling pin to compress the layers. Gently peel off the paper without disturbing the ham.
Cut the rectangle in half widthwise to make two 10x7-inch bands. Gently roll one long edge of a band into the center and then roll the opposite edge in so the two rolls meet in the middle and resemble a double scroll. Press lightly to stick the two rolls together. Repeat with the second band. (The rolls can be assembled to this point and held in the refrigerator for several hours.)
With a very sharp knife, slice each band into about 22 pieces, just under 1/2-inch each. Arrange the palmiers on two parchment-lined or nonstick baking sheets and bake until deep golden brown and no longer doughy in the center (break one open to be sure), 10 to 12 minutes. Be careful not to burn the bottoms. Let cool on a rack and serve just slightly warm or within an hour if possible.
Photo: Scott Phillips